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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 18 Nov 2013 12:44:34 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/18/t13847966915ttxt0xu9a94rf2.htm/, Retrieved Sat, 27 Apr 2024 09:26:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226186, Retrieved Sat, 27 Apr 2024 09:26:51 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2013-11-18 17:44:34] [40534ca708dbd0a01437b63d5245c315] [Current]

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Dataseries X:

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Histogram

Boxplots

-2,5
4,4
13,7
12,3
13,4
2,2
1,7
-7,2
-4,8
-2,9
-2,4
-2,5
-5,3
-7,1
-8
-8,9
-7,7
-1,1
4
9,6
10,9
13
14,9
20,1
10,8
11
3,8
10,8
7,6
10,2
2,2
-0,1
-1,7
-4,8
-9,9
-13,5
-18,1
-18
-15,7
-15,2
-15,1
-17,9
-14,5
-9,4
-4,2
-2,2
4,5
12,4
15,8
11,5
14,1
18,8
26,1
27,9
25,4
23,4
11,5
9,9
8,1
12,6
8,2
5,4
1
-2,9
-3,7
-7
-7,2
-11,8
-2,1
1,2
2,5
4,8
-6,6
-16
-22,7
-17,7
-18,2
-18,9
-16
-12,2
-17,1
-18,6
-17,5
-24,9

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226186&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226186&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226186&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.903812	8.2836	0
2	0.793009	7.268	0
3	0.646514	5.9254	0
4	0.529053	4.8488	3e-06
5	0.421382	3.862	0.00011
6	0.318663	2.9206	0.002243
7	0.207703	1.9036	0.030192
8	0.083278	0.7633	0.223723
9	-0.039811	-0.3649	0.358061
10	-0.176817	-1.6206	0.054431
11	-0.296575	-2.7182	0.003986
12	-0.392844	-3.6005	0.000268
13	-0.430493	-3.9455	8.2e-05
14	-0.439749	-4.0304	6.1e-05
15	-0.417781	-3.829	0.000124
16	-0.383703	-3.5167	0.000354
17	-0.366972	-3.3634	0.000581
18	-0.34716	-3.1818	0.001026
19	-0.32	-2.9328	0.002164

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.903812 & 8.2836 & 0 \tabularnewline
2 & 0.793009 & 7.268 & 0 \tabularnewline
3 & 0.646514 & 5.9254 & 0 \tabularnewline
4 & 0.529053 & 4.8488 & 3e-06 \tabularnewline
5 & 0.421382 & 3.862 & 0.00011 \tabularnewline
6 & 0.318663 & 2.9206 & 0.002243 \tabularnewline
7 & 0.207703 & 1.9036 & 0.030192 \tabularnewline
8 & 0.083278 & 0.7633 & 0.223723 \tabularnewline
9 & -0.039811 & -0.3649 & 0.358061 \tabularnewline
10 & -0.176817 & -1.6206 & 0.054431 \tabularnewline
11 & -0.296575 & -2.7182 & 0.003986 \tabularnewline
12 & -0.392844 & -3.6005 & 0.000268 \tabularnewline
13 & -0.430493 & -3.9455 & 8.2e-05 \tabularnewline
14 & -0.439749 & -4.0304 & 6.1e-05 \tabularnewline
15 & -0.417781 & -3.829 & 0.000124 \tabularnewline
16 & -0.383703 & -3.5167 & 0.000354 \tabularnewline
17 & -0.366972 & -3.3634 & 0.000581 \tabularnewline
18 & -0.34716 & -3.1818 & 0.001026 \tabularnewline
19 & -0.32 & -2.9328 & 0.002164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226186&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.903812[/C][C]8.2836[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.793009[/C][C]7.268[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.646514[/C][C]5.9254[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.529053[/C][C]4.8488[/C][C]3e-06[/C][/ROW]
[ROW][C]5[/C][C]0.421382[/C][C]3.862[/C][C]0.00011[/C][/ROW]
[ROW][C]6[/C][C]0.318663[/C][C]2.9206[/C][C]0.002243[/C][/ROW]
[ROW][C]7[/C][C]0.207703[/C][C]1.9036[/C][C]0.030192[/C][/ROW]
[ROW][C]8[/C][C]0.083278[/C][C]0.7633[/C][C]0.223723[/C][/ROW]
[ROW][C]9[/C][C]-0.039811[/C][C]-0.3649[/C][C]0.358061[/C][/ROW]
[ROW][C]10[/C][C]-0.176817[/C][C]-1.6206[/C][C]0.054431[/C][/ROW]
[ROW][C]11[/C][C]-0.296575[/C][C]-2.7182[/C][C]0.003986[/C][/ROW]
[ROW][C]12[/C][C]-0.392844[/C][C]-3.6005[/C][C]0.000268[/C][/ROW]
[ROW][C]13[/C][C]-0.430493[/C][C]-3.9455[/C][C]8.2e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.439749[/C][C]-4.0304[/C][C]6.1e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.417781[/C][C]-3.829[/C][C]0.000124[/C][/ROW]
[ROW][C]16[/C][C]-0.383703[/C][C]-3.5167[/C][C]0.000354[/C][/ROW]
[ROW][C]17[/C][C]-0.366972[/C][C]-3.3634[/C][C]0.000581[/C][/ROW]
[ROW][C]18[/C][C]-0.34716[/C][C]-3.1818[/C][C]0.001026[/C][/ROW]
[ROW][C]19[/C][C]-0.32[/C][C]-2.9328[/C][C]0.002164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226186&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226186&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.903812	8.2836	0
2	0.793009	7.268	0
3	0.646514	5.9254	0
4	0.529053	4.8488	3e-06
5	0.421382	3.862	0.00011
6	0.318663	2.9206	0.002243
7	0.207703	1.9036	0.030192
8	0.083278	0.7633	0.223723
9	-0.039811	-0.3649	0.358061
10	-0.176817	-1.6206	0.054431
11	-0.296575	-2.7182	0.003986
12	-0.392844	-3.6005	0.000268
13	-0.430493	-3.9455	8.2e-05
14	-0.439749	-4.0304	6.1e-05
15	-0.417781	-3.829	0.000124
16	-0.383703	-3.5167	0.000354
17	-0.366972	-3.3634	0.000581
18	-0.34716	-3.1818	0.001026
19	-0.32	-2.9328	0.002164

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.903812	8.2836	0
2	-0.130334	-1.1945	0.117817
3	-0.254616	-2.3336	0.011003
4	0.102338	0.9379	0.175482
5	-0.006112	-0.056	0.477731
6	-0.123486	-1.1318	0.130477
7	-0.125374	-1.1491	0.126894
8	-0.145749	-1.3358	0.092609
9	-0.078906	-0.7232	0.235787
10	-0.20668	-1.8943	0.030817
11	-0.082996	-0.7607	0.224491
12	0.006008	0.0551	0.47811
13	0.15341	1.406	0.081703
14	0.010354	0.0949	0.462312
15	0.034521	0.3164	0.376245
16	0.077305	0.7085	0.240294
17	-0.145466	-1.3332	0.093033
18	-0.050525	-0.4631	0.322255
19	0.028236	0.2588	0.398217

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.903812 & 8.2836 & 0 \tabularnewline
2 & -0.130334 & -1.1945 & 0.117817 \tabularnewline
3 & -0.254616 & -2.3336 & 0.011003 \tabularnewline
4 & 0.102338 & 0.9379 & 0.175482 \tabularnewline
5 & -0.006112 & -0.056 & 0.477731 \tabularnewline
6 & -0.123486 & -1.1318 & 0.130477 \tabularnewline
7 & -0.125374 & -1.1491 & 0.126894 \tabularnewline
8 & -0.145749 & -1.3358 & 0.092609 \tabularnewline
9 & -0.078906 & -0.7232 & 0.235787 \tabularnewline
10 & -0.20668 & -1.8943 & 0.030817 \tabularnewline
11 & -0.082996 & -0.7607 & 0.224491 \tabularnewline
12 & 0.006008 & 0.0551 & 0.47811 \tabularnewline
13 & 0.15341 & 1.406 & 0.081703 \tabularnewline
14 & 0.010354 & 0.0949 & 0.462312 \tabularnewline
15 & 0.034521 & 0.3164 & 0.376245 \tabularnewline
16 & 0.077305 & 0.7085 & 0.240294 \tabularnewline
17 & -0.145466 & -1.3332 & 0.093033 \tabularnewline
18 & -0.050525 & -0.4631 & 0.322255 \tabularnewline
19 & 0.028236 & 0.2588 & 0.398217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226186&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.903812[/C][C]8.2836[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.130334[/C][C]-1.1945[/C][C]0.117817[/C][/ROW]
[ROW][C]3[/C][C]-0.254616[/C][C]-2.3336[/C][C]0.011003[/C][/ROW]
[ROW][C]4[/C][C]0.102338[/C][C]0.9379[/C][C]0.175482[/C][/ROW]
[ROW][C]5[/C][C]-0.006112[/C][C]-0.056[/C][C]0.477731[/C][/ROW]
[ROW][C]6[/C][C]-0.123486[/C][C]-1.1318[/C][C]0.130477[/C][/ROW]
[ROW][C]7[/C][C]-0.125374[/C][C]-1.1491[/C][C]0.126894[/C][/ROW]
[ROW][C]8[/C][C]-0.145749[/C][C]-1.3358[/C][C]0.092609[/C][/ROW]
[ROW][C]9[/C][C]-0.078906[/C][C]-0.7232[/C][C]0.235787[/C][/ROW]
[ROW][C]10[/C][C]-0.20668[/C][C]-1.8943[/C][C]0.030817[/C][/ROW]
[ROW][C]11[/C][C]-0.082996[/C][C]-0.7607[/C][C]0.224491[/C][/ROW]
[ROW][C]12[/C][C]0.006008[/C][C]0.0551[/C][C]0.47811[/C][/ROW]
[ROW][C]13[/C][C]0.15341[/C][C]1.406[/C][C]0.081703[/C][/ROW]
[ROW][C]14[/C][C]0.010354[/C][C]0.0949[/C][C]0.462312[/C][/ROW]
[ROW][C]15[/C][C]0.034521[/C][C]0.3164[/C][C]0.376245[/C][/ROW]
[ROW][C]16[/C][C]0.077305[/C][C]0.7085[/C][C]0.240294[/C][/ROW]
[ROW][C]17[/C][C]-0.145466[/C][C]-1.3332[/C][C]0.093033[/C][/ROW]
[ROW][C]18[/C][C]-0.050525[/C][C]-0.4631[/C][C]0.322255[/C][/ROW]
[ROW][C]19[/C][C]0.028236[/C][C]0.2588[/C][C]0.398217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226186&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226186&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.903812	8.2836	0
2	-0.130334	-1.1945	0.117817
3	-0.254616	-2.3336	0.011003
4	0.102338	0.9379	0.175482
5	-0.006112	-0.056	0.477731
6	-0.123486	-1.1318	0.130477
7	-0.125374	-1.1491	0.126894
8	-0.145749	-1.3358	0.092609
9	-0.078906	-0.7232	0.235787
10	-0.20668	-1.8943	0.030817
11	-0.082996	-0.7607	0.224491
12	0.006008	0.0551	0.47811
13	0.15341	1.406	0.081703
14	0.010354	0.0949	0.462312
15	0.034521	0.3164	0.376245
16	0.077305	0.7085	0.240294
17	-0.145466	-1.3332	0.093033
18	-0.050525	-0.4631	0.322255
19	0.028236	0.2588	0.398217

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code